Seismology is used for exploration, archaeological studies, and engineering projects that require geological information. Exploration seismology provides data that, when used in conjunction with other available geophysical, borehole, and geological data, provides information about the structure and distribution of rock types and their contents. Such information greatly aids searches for water, geothermal reservoirs, and mineral deposits such as hydrocarbons and ores. Most oil companies rely on exploration seismology to select sites in which to drill exploratory oil wells.
Traditional seismology employs artificially-generated seismic waves to map subsurface structures. The seismic waves propagate from a source down into the earth and reflect from boundaries between subsurface structures. Surface receivers detect and record reflected seismic waves for later analysis. Though some large-scale structures can often be perceived from a direct examination of the recorded signals, the recorded signals must be processed to remove distortion and reveal finer detail in the subsurface image. Because this processing includes migration (a conversion of the measured time-dependent waveforms into position-dependent seismic information), the quality of the resulting subsurface image is highly dependent on the accuracy of the estimated seismic wave propagation speeds. A subsurface velocity model is used during the migration step to specify how this propagation speed varies as a function of position.
“Velocity analysis” is the term used to describe the act of extracting velocity information from seismic data. One way to perform velocity analysis is to begin with an assumed velocity model, to migrate the seismic data based on this model, and to analyze the residual curvature (“residual moveout”) of the migrated seismic data to determine errors in the assumed velocity model. The velocity model can then be updated and the process repeated until the model converges. This approach to velocity analysis is called “migration velocity analysis” or “MVA”.
The residual curvature at a given position is a function not only of the local velocity error at that position, but also of the velocity errors all along the path traversed by the seismic waves. To separate out the individual contributions to the residual curvatures, the subsurface structure can be analyzed from a tomographic perspective. See, e.g.:    Stork, C., and R. W. Clayton, 1991, Linear aspects of tomographic velocity analysis: Geophysics, 56, 483-495.    Stork, C., 1992, Reflection tomography in the postmigrated domain: Geophysics, 57, 680-692.    Liu, Z., 1997, An analytical approach to migration velocity analysis: Geophysics, 62, 1238-1249.    Meng, Z., N. Bleistein, and K. D. Wyatt, 1999, 3D analytical migration velocity analysis I: Two-step velocity estimation by reflector-normal update: 69th Annual International Meeting, SEG, Expanded Abstracts, 1727-1730.    Meng, Z., P. A. Valasek, S. A. Whitney, C. B. Sigler, B. K. Macy, and N. Dan Whitmore, 2004, 3D global tomographic velocity model building: 74th Annual International Meeting, SEG, Expanded Abstracts, 2379-2382.    Mosher, C. C., S. Jin, and D. J. Foster, 2001, Migration velocity analysis using common angle image gathers: 71st Annual International Meeting, SEG, Expanded Abstracts, 889-892.    Zhou, H., S. H. Gray, J. Young, D. Pham, and Y. Zhang, 2003, Tomographic residual curvature analysis: The process and its components: 73rd Annual International Meeting, SEG, Expanded Abstracts, 666-669.
For the most part, existing MVA techniques rely on ray-based tomography to convert the residual curvature into updates for the velocity model. The assumptions inherent in ray-based tomography cause excessive smoothing in the velocity updates, thereby limiting resolution of the resulting velocity model. To address this issue, a recent paper (Xie, X., and H. Yang, 2008, The finite-frequency sensitivity kernel for migration residual moveout: Geophysics, 73, S241-249) proposes the use of a sensitivity kernel to determine velocity model updates from relative residual moveout values. However, the velocity models produced by the method described in the paper also have limited resolution and in many cases they fail to match accepted geophysical principles.
While the disclosed embodiments susceptible to various modifications and alternative forms, specific implementations are shown by way of example in the drawings and will be described herein in detail. It should be understood, however, that the drawings and detailed description are not intended to limit the disclosed embodiments to the particular form shown, but on the contrary, the intention is to cover all modifications, equivalents and alternatives falling within the scope of the appended claims.